English

About Berge-F\"uredi's conjecture on the chromatic index of hypergraphs

Combinatorics 2024-03-15 v1

Abstract

We show that the chromatic index of a hypergraph H\mathcal{H} satisfies Berge-F\"uredi conjectured bound q(H)Δ([H]2)+1\mathrm{q}(\mathcal{H})\le \Delta([\mathcal{H}]_2)+1 under certain hypotheses on the antirank ar(H)\mathrm{ar}(\mathcal{H}) or on the maximum degree Δ(H)\Delta(\mathcal{H}). This provides sharp information in connection with Erd\H{o}s-Faber-Lov\'asz Conjecture which deals with the coloring of a family of cliques that intersect pairwise in at most one vertex.

Keywords

Cite

@article{arxiv.2403.09518,
  title  = {About Berge-F\"uredi's conjecture on the chromatic index of hypergraphs},
  author = {Alain Bretto and Alain Faisant and François Hennecart},
  journal= {arXiv preprint arXiv:2403.09518},
  year   = {2024}
}